Deconstructing the Gerber Statistic

The Gerber Statistic is a recently proposed co-movement measure that demonstrates compelling mean-variance optimisation performance relative to the sample correlation and shrinkage alternatives. However, the measure is ultimately a conditional statistic and thus, due to conditioning bias, will naturally differ from full-sample measures, likely in unexpected ways. This contribution makes use of an intuitive two-asset simulation framework to better elucidate the statistical behaviour of the Gerber Statistic, across its three proposed forms. Using graphical correlation profiles, we systematically explore the measure's behaviour across return conditioning threshold, sample size and market distribution, detailing its mechanisms of performance but also demonstrating several caveats around its understanding and use. We conclude that while interesting, the Gerber Statistic is best currently viewed as an imperfect conditional dependence metric